Analytical Results on a Wilson-Cowan Neuronal Network Modified Model

Abstract

Wilson–Cowan model is employed in studies concerning neuronal networks. This model consists of two nonlinear differential equations that represent the interaction between excitatory and inhibitory populations of neurons. The mutual influence of these populations is described through a sigmoidal function, which is usually chosen as the hyperbolic tangent or the logistic curve. Both choices make difficult theoretical analyses. Here we choose another sigmoidal function and analytically obtain the set of parameter values for which an asymptotically stable limit cycle exists. This result is potentially useful to analytical and numerical works on the binding problem, which is the problem of creating a coherent representation of objects from the oscillatory activity of spatially separated cortical columns.